Convert durations to start times

Question

Problem

I have some org-mode tables with a column containing the duration (or length) of musical tracks:

|---+---------------------------------+-----------------------------------+----------|
| # | Artist                          | Title                             | Duration |
|---+---------------------------------+-----------------------------------+----------|
| 1 | Lorem ipsum dolor sit amet      | consectetuer adipiscing elit      |     7:32 |
| 2 | Donec hendrerit tempor tellus   | Donec pretium posuere tellus      |  1:09:27 |
| 3 | Proin quam nisl, tincidunt et   | mattis eget, convallis nec, purus |    10:15 |
| 4 | Cum sociis natoque penatibus et | magnis dis parturient montes      |     4:25 |
|---+---------------------------------+-----------------------------------+----------|

I'd like to convert the durations to start times. The result of the converstion should look like this:

|---+---------------------------------+-----------------------------------+------------|
| # | Artist                          | Title                             | Start time |
|---+---------------------------------+-----------------------------------+------------|
| 1 | Lorem ipsum dolor sit amet      | consectetuer adipiscing elit      |       0:00 |
| 2 | Donec hendrerit tempor tellus   | Donec pretium posuere tellus      |       7:32 |
| 3 | Proin quam nisl, tincidunt et   | mattis eget, convallis nec, purus |    1:16:59 |
| 4 | Cum sociis natoque penatibus et | magnis dis parturient montes      |    1:27:14 |
|---+---------------------------------+-----------------------------------+------------|

Note

In the duration input

• Durations will be given in terms of hours, minutes, and seconds, separated by colons
• leading zeroes may or may not be present (ie. a duration may look like "09:25" or "9:25")
• the hours field may or may not be present (ie. a duration might look like "9:25" or "1:09:25" or even "0:09:25")

In the start time output

• minutes and seconds should always be present, even if they're zero (ex: "0:00" and "0:32" are both correct)
• if the left-most field is not a minute field and is 0, it and the colon following it should be omitted (ie. output "12:24", not "0:12:24")
• a field should be padded with leading zeroes if there is another field to its left (ie. these are all correct: "1:09:26", "1:00:26", "1:00:00", "9:26", and these are wrong: "0:09:26", "00:09:26")

Answer 1

The following provides my-durations-to-start-times to convert durations to start-times, e.g.,

(my-durations-to-start-times '("7:32" "1:09:27" "10:15" "4:25"))
;; => ("0:00" "7:32" "1:16:59" "1:27:14")

(defun my-duration-to-seconds (duration)
  "Return number of seconds of DURATION string."
  (let ((seconds 0)
        (unit 1))
    (dolist (n (nreverse (mapcar #'string-to-number (split-string duration ":"))))
      (setq seconds (+ seconds (* n unit)))
      (setq unit (* unit 60)))
    seconds))

(cl-assert (= (my-duration-to-seconds "04") 4))
(cl-assert (= (my-duration-to-seconds "7:32") (+ (* 7 60) 32)))
(cl-assert (= (my-duration-to-seconds "1:09:27") 4167))

(defun my-format-seconds (seconds)
  (let* ((h (floor seconds 3600))
         (seconds (- seconds (* 3600 h)))
         (m (floor seconds 60))
         (seconds (- seconds (* 60 m)))
         (s seconds))
    (if (zerop h)
        (format "%d:%02d" m s)
      (format "%d:%02d:%02d" h m s))))

(cl-assert (string= (my-format-seconds (my-duration-to-seconds "0")) "0:00"))
(cl-assert (string= (my-format-seconds (my-duration-to-seconds "00:09:26")) "9:26"))

(defun my-durations-to-start-times (durations)
  (let ((start 0))
    (mapcar (lambda (duration)
              (prog1 (my-format-seconds start)
                (setq start (+ start (my-duration-to-seconds duration)))))
            durations)))

(cl-assert (equal (my-durations-to-start-times '("7:32" "1:09:27" "10:15" "4:25"))
                  '("0:00" "7:32" "1:16:59" "1:27:14")))

Use my-durations-to-start-times in org-mode table formula

|---+----------+------------|
|   | Duration | Start time |
|---+----------+------------|
| 1 |     7:32 |       0:00 |
| 2 |  1:09:27 |       7:32 |
| 3 |    10:15 |    1:16:59 |
| 4 |     4:25 |    1:27:14 |
|---+----------+------------|
#+TBLFM: $>='(nth (1- (string-to-number $1)) (my-durations-to-start-times '(@2$>>..@5$>>)))